Nernst equation
In electrochemistry, the Nernst equation is an equation that relates the reduction potential of a half-cell (or the total voltage (electromotive force) of the full cell) at any point in time to the standard electrode potential, temperature, activity, and reaction quotient of the underlying reactions and species used. When the reaction quotient is equal to the equilibrium constant of the reaction for a given temperature, i.e. when the concentration of species are at their equilibrium values, the Nernst equation gives the equilibrium voltage of the half-cell (or the full cell), which is zero; at equilibrium, Q=K, ΔG=0, and therefore, E=0. It is named after the German physical chemist who first formulated it, Walther Nernst. Tossup Questions # One term in this equation is defined by the ratio of the initial concentrations in the reaction. This equation, which can be modified to analyze a membrane that is permeable to multiple ions, contains a term symbolized Q that is called the reaction quotient. The Goldman equation is a modification of this equation, which is often demonstrated by the use of a salt bridge connecting a cathode and an anode in solution. For 10 points, name this equation that calculates the potential of an electrochemical cell, named for a German. # Deviations from this equation are modeled by an equation which includes a term proportional to the log of the current density, and when that deviation is low, the Stern Geary equation modifies this equation. Another modification of this equation predicts that current will increase exponentially with applied voltage, and this equation corrects for the fact that the concentrations of reactants are seldom at one molar. This equation is modified by the Tafel and the Butler-Volmer equations. This equation calculates the change in potential as RT over nF times the ln of the reaction quotient. For 10 points, name this equation that calculates the reduction or oxidation potential of one half cell. # This equation is very similar to the equation relating the Fermi level of an n-type semiconductor and the standard dopant energy level. This equation is used to relate the partial pressure and the sensor response of a CHEMFET or a Kelvin probe. This equation is used to delineate different areas of a Pourbaix diagram. One modification of this equation adds a series of permeability coefficients and usually has a coefficient of (*) 60 mV, and is used to calculate the membrane potential of a cell. This equation, which at STP has a coefficient of 2.303, can be applied to either a half cell or a full cell. The coefficient of this equation is RT divided by zF. For 10 points, name this equation used to find reduction potentials, named for a German chemist. # This fundamental equation does not include a term that accounts for the ohmic loss caused by current flow, and that term appears in the Butler-Volmer equation. One equation often used in conjunction with this statement accounts for the flux of ions moving across a membrane. That modification calculates membrane potentials of living cells and is named for Goldman. This equation states that the product of RT over NF and the natural log of a reaction quotient yields the change in a cell's electric potential. For 10 points, name this equation that can be used to calculate equilibrium reduction potential of electrochemical half cells. # The potential of the outer Helmholtz plane is important to a modified version of this equation. That equation requires there be no surface states when considering semiconductors in solutions, and predicts that the gradient of transfer is half of that for metals in the overpotential limit. The Tafel equation comes from this equation, as does another equation that involves electrode surface area. Yet another equation derived from this one is applied to (*) cell membranes. On one side of this equation, the natural gas constant is multiplied by temperature times natural logarithm reaction quotient divided by Faraday's constant. Its variants include the Butler-Volmer and Goldman equation and it is used to determine the reduction potential of an electrochemical cell. For 10 points, name this equation central to electrochemistry.